Mathematics
Reflexive relation
Practice questions
On (A={\varnothing,{1},{2},{1,2}}), (R={(X,Y):X\subset Y\text{ or }X=Y}). What is (R) with respect to reflexivity?If (A=\mathcal{P}({1,2})) and (R={(X,Y):X\triangle Y=X}), how many diagonal pairs are in (R)?On (A={1,2,3,4,5}), (R={(a,b):a) and (b) have a common factor greater than (1)(}). Is (R) reflexive?If (A={2,4,8,16}) and ((a,b)\in R) if both (a) and (b) are divisible by a common power of (2), what is (R) with respect to reflexivity?On (A={1,2,4,8}), (R={(a,b):\text{the ratio of }a\text{ and }b\text{ is an integral power of }2}). Is (R) reflexive?If (A={1,2,3,4,5}) and (R={(a,b):a+b\leq ab}), how many diagonal pairs are in (R)?On (A={1,2,3,4,5}), (R={(a,b):a+b\leq ab}). How many pairs must be added to make (R) reflexive?If (A={0,1,2,3}) and (R={(a,b):a^3-b^3=0}), which statement about (R) is correct?On (A={0,1,2,3,4}), (R={(a,b):a^2+b^2=a+b}). How many diagonal pairs are in (R)?If (A={0,1,2,3,4}) and (R={(a,b):a^2+b^2=a+b}), how many pairs must be added to make (R) reflexive?On (A={1,2,3,4,5,6}), (R={(a,b):a-b\text{ is divisible by }6}). What is the basis for (R) being reflexive?Let (A={1,2,3,4,5,6,7,8}) and (R={(a,b)\in A\times A:a+b\text{ is divisible by }6}). What is the minimum number of pairs needed to make (R) reflexive?If (A={1,2,3,4,5,6}) and (R={(a,b):a^2+b^2\text{ is divisible by }10}), how many diagonal pairs are already in (R)?On (A={0,1,2,3,4,5}), (R={(a,b):a^2\equiv b \pmod{5}}). How many diagonal pairs are in (R)?If (A={1,2,3,4,5,6,7}) and (R={(a,b):a\equiv 3b \pmod{4}}), how many pairs must be added to make (R) reflexive?On (A={1,2,3,4,5}), (R={(a,b):a^3-b\text{ is even}}). What is the correct reason that (R) is reflexive?If (A={0,1,2,3,4}) and (R={(a,b):a^2+b=3a}), how many diagonal pairs will (R) contain?On (A={0,1,2,3,4}), (R={(a,b):a^2+b=3a}). How many pairs must be added to make (R) reflexive?If (A={1,2,3,4,5,6}) and (R={(a,b):\gcd(a,b)\text{ is even}}), how many diagonal pairs are in (R)?On (A={1,2,3,4,5,6}), (R={(a,b):\gcd(a,b)\text{ is even}}). How many diagonal pairs must be added to make it reflexive?